Induced Electric Charge

We have seen how an electroscope can be used to measure the absolute magnitude
of an electric charge. But, how can we determine the sign of the charge? In fact, this
is fairly straightforward. Suppose that an electroscope carries a charge
of unknown sign. Consider what happens when we bring a negatively
charged amber rod, produced by rubbing the rod with fur, close to the knob of the
electroscope. The excess electrons in the rod repel the free electrons in the
knob and shaft of the electroscope. The repelled electrons move as far away
from the rod as possible, ending up in the gold leaves. Thus, the charge on the
leaves becomes more negative. If the original charge on the electroscope is
negative then the magnitude of the charge on the leaves increases in the
presence of the rod, and the leaves consequently move further apart. On the
other hand, if the original charge on the electroscope is
positive then the magnitude of the charge on the leaves decreases in the presence of the rod,
and the leaves consequently move closer together. The general rule is that
the deflection of the leaves increases when a charge of the same sign is
brought close to the knob of the electroscope, and vice versa. The sign of the charge on
an electroscope can easily be
determined in this manner.

Suppose that we bring a negatively charged rod close to the knob of an
uncharged electroscope. The excess electrons in the rod repel the free electrons
in the knob and shaft of the electroscope so that they collect in the gold
leaves, which, therefore, move apart. It follows that whenever a charged object is brought
close to the knob of an uncharged electroscope, the electroscope registers a
charge. Thus, an uncharged electroscope can be used to detect electric charge
residing on nearby objects, without disturbing that charge.

Suppose that we bring a negatively charged rod close to the knob of an uncharged
electroscope which is attached, via a conducting wire, to a large uncharged
conductor. The excess electrons in the rod repel the free electrons
in the knob and shaft of the electroscope. The repelled electrons move as far away
from the rod as possible, which means that they flow down the wire into
the external conductor. Suppose that we disconnect the wire and then remove the
charged rod. By disconnecting the wire we have stranded the electrons which were
repelled down the wire on the external conductor. Thus, the electroscope, which
was initially uncharged, acquires a deficit of electrons. In other words,
the electroscope becomes positively charged. Clearly, by bringing a charged object
close to an uncharged electroscope, transiently connecting the electroscope to
a large uncharged conductor, and then removing the object, we can induce
a charge of the opposite sign on the electroscope without affecting the
charge on the object. This process is called charging by induction.

But where are we going to find a large uncharged conductor?
Well, it turns out that we standing on one.
The ground (i.e., the Earth)
is certainly large, and it turns out that it is also a reasonably
good electrical conductor. Thus, we can inductively charge an electroscope by transiently
connecting it to the ground (i.e., ``grounding'' or
``earthing'' it) whilst it is in the
presence of a charged object. The most effective way of earthing an
object is to connect it to a conducting wire which is attached, at the other end,
to a metal stake driven into the ground. A somewhat less effective way of
grounding an object is simply to touch it. It turns out that we are sufficiently
good electrical conductors that charge can flow though us to the ground.

Charges can also be induced on good insulators, although to nothing like the
same extent that they can be induced on good conductors. Suppose that a negatively
charged amber rod is brought close to a small piece of paper (which is an insulator).
The excess electrons on the rod repel the electrons in the atoms which
make up the paper, but attract the positively charged nuclei. Since paper is an
insulator, the repelled electrons are not free to move through the paper.
Instead, the atoms in
the paper polarize: i.e., they distort in such a manner
that their nuclei move slightly towards, and their electrons slightly
away from, the rod. The electrostatic force of attraction between the excess electrons in the rod
and the atomic nuclei in the paper is slightly greater than the repulsion
between the electrons in the rod and those in the paper, since the electrons in the
paper are, on average, slightly further away from the rod than the nuclei (and
the force of electrostatic attraction falls off with increasing distance). Thus,
there is a net attractive force between the rod and the paper. In fact, if the
piece of paper is sufficiently light then it can actually be picked up using the
rod. In summary, whenever a charged object is brought close to an
insulator, the atoms in the insulator polarize, resulting in
a net attractive force between the object and the insulator. This effect is
used commercially to remove soot particles from the exhaust plumes of
coal-burning power stations.